Question

You are considering making a movie. The movie is expected to cost $10.9 million up front and take a year to produce.

After that, it is expected to make $4.5 million in the year it is released and $1.9 million for the following four years. What
is the payback period of this investment? If you require a payback period of two years, will you make the movie? Does
the movie have positive NPV if the cost of capital is 10.2%?
What is the payback period of this investment?
The payback period is years. (Round to two decimal places.)

Answer 1

a) The payback period for this investment occurs in the 5th year.

b) The NPV for this investment is -$1.54 million.

The payback period describes the time it takes for an investment to generate an amount of income or cash equal to the cost of the investment.

The payback period does not consider the time value of money.

The Net Present Value (NPV), which discounts future cash flows with the cost of capital, is a more sophisticated method to evaluate an investment.

The payback period:

Year 0 (initial investment): -$10.9 million

Year 1 (release year): +$4.5 million

Year 2: +$1.9 million

Year 3: +$1.9 million

Year 4: +$1.9 million

Year 5: +$1.9 million

The cumulative cash flow:

Year 0: -$10.9 million

Year 1: -$10.9 million + $4.5 million = -$6.4 million

Year 2: -$6.4 million + $1.9 million = -$4.5 million

Year 3: -$4.5 million + $1.9 million = -$2.6 million

Year 4: -$2.6 million + $1.9 million = -$0.7 million

Year 5: -$0.7 million + $1.9 million = $1.2 million

Thus, the payback period is in the 5th year.

The NPV can be calculated using the formula:

Formula

`\text{NPV} = (R_(t))/((1+i)^(t))` -
`C_o`

`\text{NPV}` = net present value

`R_(t)` = the net cash inflow during the period t

`i` = the discount rate or cost of capital

`{t}` = time of the cash flow

`C_o` = the initial investment

Cost of capital = 10.2% = 0.102 (10.2/100)

NPV = -$10.9 million + $4.5 million / (1 + 0.102) + $1.9 million / (1 + 0.102)^2 + $1.9 million / (1 + 0.102)^3 + $1.9 million / (1 + 0.102)^4 + $1.9 million / (1 + 0.102)^5

NPV = -10.9 + 4.09 + 1.66 + 1.41 + 1.19 + 1.01

NPV = -$1.54 million